Quantum mechanics

• Solved exercises
• Oral exam notes

Course description

Kvantna mehanika is a required course for third-year undergraduates in the FMF physics program. These notes are from the winter semester of the 2020-21 academic year, when the course was taught by professor Anton Ramšak (lecture) and asst. professor Tomaž Rejec (exercises). The course covers the Copenhagen interpretation of quantum mechanics at an upper-undergraduate level; specific material includes:

• properties of the Schrödinger equation and wave function for a single particle
• the Dirac formalism; operators and bra-ket notation
• the quantum harmonic oscillator
• symmetries: translation, rotation, parity and time reversal
• properties, eigenvalues, and eigenfunctions of the angular momentum operator
• behavior of quantum particles in a central potential; the Coulomb potential and the hydrogen atom
• behavior of charged particles in a magnetic field: Zeeman coupling, Landau levels, and the Aharonov-Bohm effect
• spin and addition of angular momentum; spinors; the Pauli matrices
• perturbation theory: the first- and second-order nondegenerate case; the first-order degenerate case; time-dependent perturbation theory and Fermi’s golden rule
• scattering